A couple of the team looked momentarily bemused, as if sensing an ironic tone in the cheers; but they were as genuine as the action which had preceded them in an FA Cup fourth qualifying round witnessed by 522 spectators.
"This is the furthest we have got in the FA Cup and we just want to show our appreciation," said Sue Ayres, Thatcham's membership secretary. "They deserve to have a clap."
Ayres, a Thatcham follower for 10 years, was one of the few not drinking in the bar. When she and the 47 other occupants of the visiting supporters' coach got back to their ground, near Reading, she was due to drive a minibus ferrying club guests to their separate destinations.
"Because you are involved in the club and do things for the club, you feel involved with the players," she said.
Meanwhile the players, savouring that first lager by now, were beginning to joke about an afternoon which had seen them concede as many goals in 90 minutes as they had in their 11 matches so far this season in the Jewson Wessex League, of which they are the champions.
Thatcham's unprecedented Cup run had taken them past two teams from a higher level including Gloucester City, second in the Dr Martens - latest incarnation of the Southern League - Premier Division. But now the beautiful illogic of the Cup had given out on them.
Boreham Wood are an upwardly mobile force, having narrowly missed winning the Icis - latest incarnation of the Isthmian - Premier Division title last season after promotion the year before.
Their team - leaner and fitter than the men of Thatcham - was full of players with experience of some kind with League clubs. The speed of Anthony "Junior" Samuels, top goalscorer for the last two seasons, was demonstrably too much for the Thatcham defence, which was crucially diminished shortly before half-time by the dismissal of the team captain, Richie Hayward, for a deliberate handball which may or may not have prevented a goal being scored.
The decision by the referee - Mr S G Clingo of Wisbech - was at least debateable. Had it occurred in the Premiership or Nationwide League, there would no doubt have been outbursts of bile and routine obscenity. But this was non-League.
"That is ridiculous," exclaimed one of the Thatcham directors. "That is stupid."
A childish voice added: "Where's your glasses, referee?"
By that time, however, Thatcham were already 2-0 down and devoid of ideas. And in Terry Robbins, the 31-year-old former Welling United and Barnet forward, Boreham Wood had just the man to take advantage.
Robbins, who works at the merchant bankers Lazard Brothers as a cash administrator, finished with a smartly taken hat-trick that brought back memories of former Cup glories.
As a Welling player he reached the third round, losing 1-0 to Blackburn Rovers. There were other Cup endeavours to remember, including a win over Gillingham and taking Reading to two replays.
"It's an old cliche," he said. "But before the game I was saying to the lads that there is a great feeling about the FA Cup because there is no other competition in the world like it. When we were having our runs at Welling the crowds doubled there and we had three or four very good years at the club."
Boreham Wood, who have already improved their ground to Vauxhall Conference standards in anticipation of possible further promotion, could do with a similar lift. With the best will in the world, average crowds of around 300 cannot generate sufficient funds to sustain progression.
Having reached the FA Cup first round proper for only the third time in their history, the Hertfordshire club's players and supporters had just over 20 minutes to dream of a pairing with League opponents before the televised draw ended any speculation.
The consensus among the fans packed into the smoky back-room bar was that a home tie with Millwall, Orient or Barnet would be favourite.
As the dead tones of the FA chief executive, Graham Kelly, confirmed a home draw for Boreham Wood, a gathering roar emerged from the smokers and drinkers. We're in there! We're on telly! Bring on the big boys!
The roar diminished to a low groan at the pairing with Rushden & Diamonds, of the Conference.
"Very disappointing," said Clive Drinkall, who saw Boreham Wood's previous Cup runs in 1973/74 and 1977/78.
Robbins was more inclined to optimism. "It would have been nice to get a League club," he said. "But now we have got a good chance of getting through to the second round.
"As a non-League club you know you are never going to win the FA Cup. The thing is to get as far as you can..."
And imagine those thrilling Kelly tones as the challengers thin out. "Boreham Wood will play Liverpool... will play Tottenham Hotspur... will play Manchester United..."
FA Cup first-round draw
Carlisle Utd v Shepshed Dynamo; Blackpool v Wigan Athletic; Chesterfield v Bury; Macclesfield Town v Rochdale; Scunthorpe Utd v Rotherham Utd; Whitby Town v Hull City; Burnley v Lincoln City; Boston Utd v Lancaster City or Morecambe; Colwyn Bay v Wrexham; Northwich Victoria v Walsall; Preston North End v Barrow or Altrincham; Runcorn v Darlington; Crewe Alexandra v Kidderminster Harriers; Shrewsbury Town v Scarborough; Chester City v Stalybridge Celtic; Hartlepool Utd v York City; Mansfield Town v Consett; Stockport County v Doncaster Rovers; Newcastle Town v Notts County; Hednesford Town v Spennymoor United or Southport; Northampton Town v Watford; Colchester United v Wycombe Wanderers; Leyton Orient v Merthyr Tydfil; Cardiff City v Hastings or Hendon; Woking v Millwall; Ashford Town (Kent) v Dagenham & Redbridge; Plymouth Argyle v Fulham; Peterborough Utd v Bath City or Cheltenham Town; Gillingham v Hereford Utd; Bromley v Enfield; Cambridge Utd v Welling Utd; Torquay United v Luton Town; Swansea City v Bristol City; Borehamwood v Rushden & Diamonds; Stevenage v Hayes; Sudbury Town v Brighton and Hove Albion; Wisbech Town v St Albans City; Farnborough Town v Barnet; Bristol Rovers v Exeter City; Brentford v AFC Bournemouth.
Ties to be played weekend of 15/16/17 November.